6 papers
Greedy multiscale kernel algorithms
Sara Avesani, Armin Iske, Michael Multerer +1
Multiscale kernel approximation and greedy kernel algorithms are two established tools for scattered data approximation. We combine them into greedy multiscale kernel algorithms, i…
Samplet compression for conditionally positive definite kernels and universal Kriging
Sara Avesani, Rüdiger Kempf, Michael Multerer +1
We present a samplet-based framework for the efficient numerical solution of saddle-point systems arising from conditionally positive definite (CPD) kernel approximation in general…
Tree-Adaptive Multiscale Kernel Lasso in Samplet Coordinates
Sara Avesani, Gaia Fumagalli, Michael Multerer +1
We develop a novel framework for sparse multiscale kernel approximation of large scattered data problems based on a samplet representation. Samplets form a multiresolution analysis…
Sobolev Algorithm for Local Smoothness Analysis (SALSA) via Sharp Direct and Inverse Statements
Sara Avesani, Leevan Ling, Francesco Marchetti +1
We extend sharp direct and inverse approximation statements for kernel-based methods for finitely smooth kernels, i.e. those whose native spaces are norm-equivalent to Sobolev spac…
Multiresolution local smoothness detection in non-uniformly sampled multivariate signals
Sara Avesani, Gianluca Giacchi, Michael Multerer
Inspired by edge detection based on the decay behavior of wavelet coefficients, we introduce a (near) linear-time algorithm for detecting the local regularity in non-uniformly samp…
Multiscale scattered data analysis in samplet coordinates
Sara Avesani, Rüdiger Kempf, Michael Multerer +1
We study multiscale scattered data interpolation schemes for globally supported radial basis functions with focus on the Matérn class. The multiscale approximation is constructed t…